Research on an Improved Medical Image Enhancement Algorithm Based on P-M Model

Image enhancement can improve the detail of the image and so as to achieve the purpose of the identification of the image. At present, the image enhancement is widely used in medical images, which can help doctor’s diagnosis. IEABPM (Image Enhancement Algorithm Based on P-M Model) is one of the most common image enhancement algorithms. However, it may cause the lost of the texture details and other features. To solve the problems, this paper proposes an IIEABPM (Improved Image Enhancement Algorithm Based on P-M Model). Simulation demonstrates that IIEABPM can effectively solve the problems of IEABPM, and improve image clarity, image contrast, and image brightness.


INTRODUCTION
In the field of image process, image enhancement is a very important research direction, which has been widely used in military, remote sense, public safety, biomedicine, etc [1]. In the field of medicine, the image is usually gathered by CT machine, ultrasonic apparatus, and so on. The collected images may be blurry, which will affect diagnoses of the illness. To improve the quality of the collected images, image enhancement is used [2].
From the aspect of the realization, the image enhancement algorithm can be divided into five categories: image enhancement algorithm base on traditional theory, image enhancement algorithm based on multiscale analysis [3], image enhancement algorithm based on fuzzy theory [4], image enhancement algorithm based on humanoid vision [5] and image enhancement algorithm based on mathematic morphology [6]. Among them, the image enhancement algorithm based on mathematic morphology consists of closing operation, erosion operation, dilation operation and open operation. IEABPM (Image Enhancement Algorithm Based on P-M Model) is one of the most used [7,8]. IEABPM can effectively remove the noise of images, however, for the area which has rich textures, it may it may cause the lost of the texture details and other features. To solve the problem, IIEABPM (Improved Image Enhancement Algorithm Based on P-M Model) is proposed. And Simulation demonstrates that IIEABPM can improve image clarity, image contrast, entropy and iamge brightness.

IIEABPM
In IIEABPM, it firstly uses the normalization method to translate P-M model into posed problem. Secondly, a moderator is added to control the process of optimization. Thirdly, *Address correspondence to this author at the The College of Information Science and Engineering, Hebei North University, Zhangjiakou, Hebei, 075000, China; Tel: 0313-4029808; E-mail: 41905108@qq.com according to different region status of the image, IIEABPM chooses the spread function. To meet the performance requirements, the spread function is corrected through four steps. The first step is increasing gradient threshold. The second step is modifying spread function. The third step is adding gradient fidelity term. The last step is adding strength coefficient. Fig. (1) gives the flow chart of IIEABPM. According to Fig. (1), when the normalization is used, Gaussian kernel is adopted to smooth the images.
, and G is a Gaussian function, whose mean value and variance are respectively 0 and 2 .
After the normalization, P-M model is translated into posed problem, and there is only one continuous solution, which depends on the initial value 0 ( , ) u x y . And then a moderator is added to control the process of optimization, and 0 0 Therefore, the mathematical model of image enhancement can be written as follows: Where u is the image at time t, div means divergence operator, t u is the gradient of the image, ( ) t g u is the spread fuction, whose value means the strength of spread. n some area of the image, the value of t u decides whether or not the image is smooth. That is to say, When the value of t u is smaller, the image in the region is smoother.
In order to keep the anisotropic diffusion of spread function, t u must make spread function satisfy the following two conditions: (1) The spread of the noise is within the relatively smooth featured area; (2) The spread is not done between two adjacent areas to preserve the edge details.
When removing the noise of the image, spread function can be chosen from two kinds of expressions:

The First Step
Although the above spread model has good effects on the image denoise, its effect isn't ideal when the noise is high. To solve the problem, Eq. 3 and Eq.4 can be modified: Where 1 k , 2 k , 3 k are the gradient thresholds , and Fig. (2) gives the relationships between spread function and gradient.
From Fig. (2), we can see that the gradient and spread function has an inverse relationship. And compared with Eq.

The Second Step
In order to more accurately control the smoothness, Therefore, divergence operator can be written as: When calculating 0 G u , the similarity functional of two signals is: Where and are weight coefficients, is the gradient fidelity term, which try to make the changes of the gradient keep consistent with 0 ( ) G u . Fig. (2). Gradient vs. Spread Function.

The Third Step
In Eq. 9, gradient fidelity term is added to increase the smoothness of the image. However, whether it will impede the optimal solution has not been proved. If ( ) E u is the convex function, the optimal solution uniquely exists.
An image can be regarded as the surface in twodimensional space. The aim of using the gradient fidelity term is to keep the constraint of the continuity of the image topology. In the iterative computation, the gradient fidelity term maintains consistency of the original image and enhanced image, which can eliminate the loss of the image texture details and other features. Based on above analysis, Eq. 8 can be modified as: Where is the weight coefficient, 0 > .

The Fourth Step
To increase detailed information, the strength coefficient is added in the spread model. The model is: Where w the strength coefficient, div is means divergence operator.

Enhancement Effect Analysis
To verify the effectiveness of IIEABPM, enhancement effect tests are done, as shown in Fig. (3).

Performance Analysis
To further analyze the performance of IIEABPM, three tests are designed.
In the first test, Fig. 3(b1) is chosen as the subject, the performance of IEABPM and IIEABPM are compared in terms of the clarity, contrast, brightness and entropy. Fig. (4) gives the enhanced iamges, and Table 1 gives features of the enhaced images. . (3). Enhancement effect.
From Fig. (4) and Table 1, we can see that the performance of IIEABPM is better than that of IEABPM. In the second test, Fig. 4(a) with noise is chosen as the subject. The performance of image enhancement by the median filter, image enhancement by Gaussian filter, image enhancement by wavelet filter, IIEABPM and IEABPM are compared in the term of the enhancement effect, as shown in Fig. (5).
From Fig. (5), we can see that the performances of IE-ABPM and IIEABPM are better than the performances of the other. In Fig. 5(e), many details are removed. However, in Fig. 5(f), not only is the image noise is restrained, but also are details reserved.
In the third test, Fig. 3(a) is chosen as the subject. The performance of image enhancement by the median filter, image enhancement by Gaussian filter, image enhancement by wavelet filter, IIEABPM and IEABPM are compared in the term of the enhancement effect, as shown in Fig. (6).  Fig. (6). Compared results for rib image.